z^2+z+0.5=0

Solution for z^2+z+0.5=0 equation:

Simplifying
z2 + z + 0.5 = 0

Reorder the terms:
0.5 + z + z2 = 0

Solving
0.5 + z + z2 = 0

Solving for variable 'z'.

Begin completing the square.

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + z + -0.5 + z2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + z + z2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + z + z2 = 0 + -0.5
z + z2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
z + z2 = -0.5

The z term is z.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
z + 0.25 + z2 = -0.5 + 0.25

Reorder the terms:
0.25 + z + z2 = -0.5 + 0.25

Combine like terms: -0.5 + 0.25 = -0.25
0.25 + z + z2 = -0.25

Factor a perfect square on the left side:
(z + 0.5)(z + 0.5) = -0.25

Can't calculate square root of the right side.

The solution to this equation could not be determined.